COLUMBIA, South Carolina (CNN) -- Arizona Sen. John McCain gained an important victory Saturday in the South Carolina Republican primary, but exit polls indicate he made few inroads into the conservative heart of the Republican Party.

John McCain celebrates his victory in the South Carolina primary Saturday night.

The results leave the race for the party's presidential nomination wide open going into the January 29 primary in Florida and the "Super Tuesday" contests beyond.

"I just would have to regard this as a good night for McCain, with some significant concerns when you get into the weeds," political analyst Stuart Rothenberg told CNN.

McCain overcame a strong showing by former Arkansas Gov. Mike Huckabee among the evangelical Christian voters who dominated the day's turnout.

Huckabee, the winner of the January 3 Iowa caucuses, led widely among the self-described evangelicals who made up nearly 60 percent of the vote, according to exit polls. The Baptist pastor-turned-governor sharply emphasized his conservative Christian credentials in the state and was the choice of 40 percent of those voters.

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He has not renounced that stand, but told voters he has learned that Republican voters want border control first.

Exit polls found McCain won a narrow majority of self-described moderates, who made up about a quarter of the South Carolina turnout, and ran roughly even with Huckabee at 32 percent among people who described themselves as "somewhat conservative" -- about a third of Saturday's voters.

But he trailed both Huckabee and former Tennessee Sen. Fred Thompson among "very conservative" voters, another third of those who turned out.

Thompson campaigned heavily among evangelical Christians in upstate counties around Spartanburg and Greenville, and his third-place showing may have taken away votes that otherwise would have boosted Huckabee, Rothenberg said.

Despite his showing Saturday, Thompson is short of cash and sinking in national polls. While he remains in the race, two sources told CNN that "it was abundantly evident to all of us" that he needed a win or a very competitive second place in South Carolina to stay viable.

"We are not blind to the obvious," said one senior campaign adviser.

Analysts say Thompson was hurt by his late entry into the race, which came months after other Republicans started campaigning.

"He's really been good lately, but it's too late," CNN analyst Bill Bennett said. "If you're a Southern conservative and you can't make it in South Carolina, it's over."

As he did in 2000, McCain won this year's New Hampshire primary in an upset over a better-financed rival, George W. Bush in 2000 and Romney this time. But eight years ago, his campaign withered in a brutal campaign in South Carolina that left the Arizona senator blasting leading religious conservatives as "agents of intolerance."

This time, McCain "is benefiting from the fact that the vote has fractured so many ways," Rothenberg said. His strength remains with moderate voters, veterans and independents, but "it doesn't look to me as though he has broadened his appeal."

"Once again, he's not getting conservatives and he's not growing his share among Republicans the way I'm sure he'd hoped to," Rothenberg said.

Romney won the other contest of the day, the Nevada caucuses, and remains well-financed. He also won the GOP primary in his native Michigan on Tuesday and the largely overlooked caucuses in Wyoming on January 5.

Bennett said a victory in South Carolina, the first major contest in the heavily Republican South, was a must for Huckabee.

"If he doesn't win South Carolina, he's not going to finish anywhere close to winning in Florida," Bennett said. Watch Huckabee pump up his supporters after taking second in South Carolina »

Huckabee ran a close second in South Carolina and won Iowa, also with a strong turnout from his fellow evangelicals, but placed third in New Hampshire and Michigan and fifth in Nevada.

And in Florida, the GOP contenders will include former New York Mayor Rudy Giuliani, who abandoned the early states. He's banking on the contests in Florida and in delegate-rich states like New York, New Jersey, California and Illinois, which are among about two dozen states holding primaries and caucuses on February 5.

But Saturday has given McCain new momentum going into those battles, Bennett said.

"It's a heck of an achievement," Bennett said. "And I think he is clearly the front-runner. He is ahead in Florida now, before this win, and I think this gives him a strong wind at his back."E-mail to a friend